Diana has some mochi balls and candy canes. If she packs a mochi ball and a candy cane in each bag, there will be 14 candy canes left. If she packs 2 mochi balls and 3 candy canes in each bag, there will be 13 mochi balls left. How many mochi balls and candy canes does she have in all?
| |
Case 1 |
Case 2 |
| |
Mochi Balls |
Candy Canes |
Mochi Balls |
Candy Canes |
| Before |
1 u |
1 u + 14 |
2 p + 13 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
14 |
13 |
0 |
The number of mochi balls at first is the same for Case 1 and 2.
The number of candy canes at first is also the same for Case 1 and 2.
1 u = 2 p + 13 --- (1)
1 u + 14 = 3 p
1 u = 3 p - 14 --- (2)
(2) = (1)
3 p - 14 = 2 p + 13
3 p - 2 p = 13 + 14
1 p = 27
Total number of mochi balls and candy canes
= (2 p + 13) + 3 p
= 5 p + 13
= 5 x 27 + 13
= 135 + 13
= 148
Answer(s): 148
